| 序号 | 论文标题 | 第一作者/通信作者 | 作者机构 | 引用评价机构 | 突破性评价引用句 | | 1 | Geometric measures in the dual brunn-minkowski theory and their associated minkowski problems | 黄 勇 | 湖南大学 | 纽约大学;麻省理工学院;北京工商大学;西华盛顿大学;匈牙利科学院;柏林工业大学;湖北民族大学;加拿大纽芬兰纪念大学 | (1) In the recent revolutionary work [32], Huang-LYZ discovered fundamental geometric measures, duals of Federer’s curvature measures, called dual curvature measures C j (K,·), in the dual Brunn-Minkowski theory.
(2)In a groundbreaking work[24], Huang-LYZ discovered a new family of geometric measures called dual curvature measures Cq (K,·) and the variational formula that leads to them.
(3)In a recent groundbreaking work[24], Huang, Lutwak, Yang, and Zhang (Huang-LYZ) discovered that Aleksandrov Received by the editors August 13,2018, and, in revised form, January 15,2019.
(4)In the recent groundbreaking work[33], Huang, Lutwak, Yang and Zhang introduced dual curvature measures and found their associated variational formulas for the first time. These new curvature measures were proved to connect two different known measures, namely cone-volume measure and Alexandrov integral curvature.
(5)Recent seminal work of Huang et al.[22] brought new ingredients, the qth dual curvature measures, to the family of Minkowski problems.
(6)This missing link was recently established in the ground-breaking paper[25] by Huang, Lutwak, Yang and Zhang. Let ρ K be the radial function (see Section 2 for the definition) of a convex body K ∈ K n o.
(7)This missing link was recently established in the ground-breaking paper[31] by Huang, Lutwak, Yang and Zhang.
(8)Our work is inspired by the recent groundbreaking work of Huang et al.[13]and Lutwak et al.[21].
(9)However, it is only very recent that the dual curvature measures, which are dual to the surface area measures, were discovered in the seminal work[23] by Huang et al.
(10)Recently, Huang et al. posed the dual Minkowski problem for the qth dual curvature measure in their seminal work [14].
(11)Arising from dual quermassintegrals is a new family of geometric measures, dual curvature measures C q (K,·) for q ∈ R, discovered by Huang, Lutwak, Yang & Zhang (Huang-LYZ) in their groundbreaking work [26]. | | 2 | Solving high-dimensional partial differential equations using deep learning | Weinan, E. | 北京大数据研究院 | 宾夕法尼亚大学;
斯坦福大学 | (1)The 2 pioneering papers [HJE18; EHJ17] propose a neural-networks based technique called Deep BSDE, which was the first serious attempt for using machine learning methods to solve high dimensional PDEs.
(2)The idea of solving high-dimensional PDEs and control problems with neural networks has been pioneered by the works [33,48,49] and has been further investigated by [77].
(3)In fact, Sirignano and Spiliopoulos [16] and Han et al. [5] have demonstrated that neural networks can be used to solve partial differential equations in hundreds of dimensions, which is a revolutionary result. | | 3 | On the birationality of complete intersections associated to nef-partitions | 李 展 | 北京大学 | 德雷塞尔大学;
阿尔伯塔大学;
剑桥大学 | (1)This completes the progress in this direction made by Li’s breakthrough [Li16] by proving the result in full generality and without assumptions.
(2)This completes the groundbreaking work of Li [Li16] by removing any need for the assumptions that the Calabi- Yaus and a certain determinantal variety are irreducible. | | 4 | Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations | Weinan, E. | 北京大学;
北京大数据研究院 | 山东大学;
埃默里大学 | (1)In a recent breakthrough paper of E et al [7], they solved the BSDEs from a control perspective by regarding the Z term as a control.
(2)The idea of solving high-dimensional PDEs and control problems with neural networks has been pioneered by the works [33,48,49] and has been further investigated by[77]. | | 5 | The nonvanishing hypothesis at infinity for rankin-selberg convolutions | 孙斌勇 | 中国科学院 | 哈尔滨工业大学;印度科学教育与研究学院 | (1)Finally,we remark that although we have followed Sun’s pioneering paper [16] closely for the general approach,there are still many delicate analyses to carry out in our case.
(2)Recently, Sun made a breakthrough by confirming it for GL n (R) × GL n-1 (R) and GL n (C) × GL n-1 (C); see [16]. | | 6 | Stability of fractional-order nonlinear dynamic systems lyapunov direct method and generalized mittag-leffler stability | 李 岩 | 山东大学 | 北京交通大学;加利福尼亚大学美塞德分校;安徽大学 | (1)In the seminal work [1], the Lyapunov direct method is proposed by use of where is the Caputo fractional derivative.
(2)The Mittag-Lefer stability de nition is pro- posed to describe the dynamics of the system, and the fractional direct Lyapunov method is introduced creatively in [15,16],which inspired many scholars and derived a series of pioneering work. | | 7 | New sum-product type estimates over finite fields | Roche Newton, Oliver | 武汉大学 | 洛桑理工学院;
新南威尔士大学 | (1)In a breakthrough paper[8], Roche-Newton, Rudnev, and Shkredov improved and general-ized this result to arbitrary fields.
(2)A major breakthrough came from the work of Roche-Newton, Rudnev and Shkredov[14] which is based on Rudnev’s point plane incidence bound [16] and states that if |A| 6 p 5/8 then max{|A + A|,|AA|} ≫ |A| 6/5.(3) We note that the idea of applying geometric incidence estimates to sum-product type problems is due to Elekes [4]. |
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